This proposal develops sequential designs for dose-finding clinical trials and association studies in genetics. The new methods are developed in situations where there are no existing methods or existing methods are not efficient. All research projects described below were motivated by one or more clinical trials at the Lineberger Comprehensive Cancer Center. The clinical settings are the following: (1) In the first setting, a dose-finding trial for a cytostatic agent is conducted. The outcome is bivariate binary, toxicity and therapeutic response. The goal is to find the optimal biological safe dose, the dose defined as the minimum of the dose with a specified toxicity rate and the dose with a specified response rate. (2) In the second setting, a dose- finding trial in oncology is conducted to find the dose with a certain rate of dose limiting toxicity. Toxicity outcome is binary and patients are followed for toxicity for a long period of time. The goal is to develop flexible and efficient designs for such trials. (3) In the third setting toxicity outcome is ordinal. The goal is to develop a study design to identify the dose with a target weighted average of the rates of different toxicity grades. (4) The fourth setting is a genome-wide association study. [unreadable] [unreadable] [unreadable]